Power Rule in Calculus

The power rule in calculus is a fundamental rule used for finding the derivative of a function that is in the form of f(x) = x^n, where n is a constant. The power rule states that the derivative of f(x) = x^n with respect to x is f'(x) = nx^(n-1).

Study Guide for Power Rule

Here are the steps to follow when applying the power rule:

1. Identify the exponent: Look for the exponent in the function. It should be in the form of x^n.
2. Apply the power rule: Once you have identified the exponent, apply the power rule by multiplying the exponent by the coefficient and then reducing the exponent by 1.
3. Write the derivative: After applying the power rule, write the derivative of the function.
4. Example: Let's find the derivative of f(x) = 3x^2 using the power rule.

First, we identify the exponent, which is 2. Then, we apply the power rule by multiplying the exponent by the coefficient, giving us 6, and then reducing the exponent by 1, giving us f'(x) = 6x^(2-1) = 6x.

Remember to practice using the power rule with different functions to become comfortable with it.

Hope this helps! Let me know if you have any other questions.